Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle FCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{EF} \cong \overline{AB}$ $, \ $ $ \angle CEF \cong \angle BAC$ $, \ $ $ \angle ECF \cong \angle ACB$ $, \ $ $ \overline{CE} \cong \overline{DE}$ $, \ $ $ \angle ECF \cong \angle BDE$ $, \ $ and $\ $ $ \angle CFE \cong \angle DBE$ Proof $ \triangle BCA \cong \triangle FCE$ because AAS $ \overline{BC} \cong \overline{CF}$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle BCE$ because SAS $ \angle BCE \cong \angle CEF$ because alternate interior angles are equal $ \angle BAC \cong \angle BEC$ because corresponding parts of congruent triangles are congruent $ \triangle BCE \cong \triangle FCE$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle BCE \cong \triangle BCA$ is the first wrong statement.